Sobolev Spaces

Dumitru Motreanu, Viorica Venera Motreanu and Nikolaos Papageorgiou
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Dumitru Motreanu: University of Perpignan, Department of Mathematics
Viorica Venera Motreanu: Ben-Gurion University of the Negev, Department of Mathematics
Nikolaos Papageorgiou: National Technical University, Department of Mathematics

Chapter Chapter 1 in Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 2014, pp 1-13 from Springer

Abstract: Abstract This chapter provides a comprehensive survey of the mathematical background of Sobolev spaces that is needed in the rest of the book. In addition to the standard notions, results, and calculus rules, various other useful topics, such as Green’s identity, the Poincaré–Wirtinger inequality, and nodal domains, are also discussed. A careful distinction between various properties of Sobolev functions is made with respect to whether they are defined on a one-dimensional interval or a multidimensional domain. Bibliographical information and related comments can be found in the Remarks section.

Keywords: Sobolev Space; Chain Rule; Lipschitz Continuous Function; Sobolev Function; Nodal Domain (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-9323-5_1

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DOI: 10.1007/978-1-4614-9323-5_1

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